in 1997, fang proposed the concept of boundedness of $l$-fuzzy setsin $l$-topological vector spaces. since then, this concept has beenwidely accepted and adopted in the literature. in this paper,several characterizations of bounded $l$-fuzzy sets in$l$-topological vector spaces are obtained and some properties ofbounded $l$-fuzzy sets are investigated.

A binary poset code of codimension m (of cardinality 2n−m , where n is the code length) can correct maximum m errors. All possible poset metrics that allow codes of codimension m to be m-, (m − 1)-, or (m − 2)-perfect are described. Some general conditions on a poset which guarantee the nonexistence of perfect poset codes are derived; as examples, we prove the nonexistence of r-perfect poset co...

We study a poset N on the free monoid X∗ on a countable alphabet X. This poset is determined by the fact that its total extensions are precisely the standard term orders on X ∗. We also investigate the poset classifying degree-compatible standard term orders, and the poset classifying sorted term orders. For the latter poset, we give a Galois coconnection with the Young lattice.

The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when U is an Lfuzzy quasi-uniformity and they will be coincident when U ...

In this paper we study the spectral resolution of the Laplacian L of the Koszul complex of the Lie algebras corresponding to a certain class of posets. Given a poset P on the set {1, 2, . . . , n}, we define the nilpotent Lie algebra LP to be the span of all elementary matrices zx,y, such that x is less than y in P . In this paper, we make a decisive step toward calculating the Lie algebra homo...

The concepts of fuzzy source and fuzzy successor operators for an L-fuzzy automaton (L is a latticeordered monoid) are introduced, which turn out to be L-fuzzy closure operators. When L is a quantale, these operators introduce L-fuzzy topologies. These observations are then used to give topological characterization of the separatedness and connectedness properties of an L-fuzzy automaton. c ©20...

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...

An antimatroid is a family of sets which is accessible, closed under union, and includes an empty set. A number of examples of antimatroids arise from various kinds of shellings and searches on combinatorial objects, such as, edge=node shelling of trees, poset shelling, node-search on graphs, etc. (Discrete Math. 78 (1989) 223; Geom. Dedicata 19 (1985) 247; Greedoids, Springer, Berlin, 1980) [1...

The notion of separatedness degrees of L-fuzzy subsets is introduced in L-fuzzy topological spaces by means of L-fuzzy closure operators. Furthermore, the notion of connectedness degrees of L-fuzzy subsets is introduced. Many properties of connectedness in general topology are generalized to L-fuzzy topological spaces.